Method and Apparatus for Determining Cardiac Performance in a Patient with a Conductance Catheter

ABSTRACT

An apparatus for determining cardiac performance in the patient involving a conductance catheter ( 12 ) for measuring conductance and blood volume in a heart chamber of the patient. The apparatus includes a processor ( 14 ) for determining instantaneous volume of the ventricle by applying a non-linear relationship between the measured conductance and the volume of blood in the heart chamber to identify mechanical strength of the chamber. The processor ( 14 ) is in communication with the conductance catheter ( 12 ).

This invention was made with government support under National Instituteof Health (NIH) Grant No. STTR (HL 67475-01). The government may havecertain rights in the invention.

FIELD OF THE INVENTION

The present invention is related to measuring instantaneous ventricularvolume in the heart of a patient. More specifically, the presentinvention is related to measuring instantaneous ventricular volume inthe heart of a patient by removing the contributor to conductance ofmuscle, and applying a non-linear relationship to the measuredconductance and the volume of blood in the heart.

BACKGROUND OF THE INVENTION

Measurements of electrical conductance using a tetrapolar admittancecatheter are used to estimate instantaneous ventricular volume inanimals and humans. The measurements of volume are plotted againstventricular pressure to determine several important parameters ofcardiac physiologic function. A significant source of uncertainty in themeasurement is parallel conductance due to current in the ventricularmuscle. The estimated volume is larger than the blood volume alone,which is required for the diagnostic measurement. Furthermore,presently, a linear relationship between conductance and estimatedvolume is used to calibrate the measurements. The actual relationship issubstantially nonlinear.

The invention comprises an improved method for estimating instantaneousblood volume in a ventricle by subtracting the muscle contribution formthe total conductance measured. The method relies on measuring thecomplex admittance, rather than apparent conductance (admittancemagnitude), as is presently done. Briefly, the improvement consists ofmeasuring the phase angle in addition to admittance magnitude and thendirectly subtracting the muscle component from the combined measurement,thereby improving the estimate of instantaneous blood volume. Thetechnique works because the electrical properties of muscle arefrequency-dependent, while those of blood are not. We propose thiscalibration technique as a substantial improvement in clinical andresearch instrumentation calibration methods.

The invention comprises an improved method for estimating instantaneousvolume of a ventricle by applying a nonlinear relationship between themeasured conductance and the volume of blood in the surrounding space.The nonlinear calibration relation has been determined from experimentsand numerical model studies. This calibration technique is a substantialimprovement in clinical and research instrumentation calibrationmethods.

SUMMARY OF THE INVENTION

The present invention pertains to an apparatus for determining cardiacperformance in the patient. The apparatus comprises a conductancecatheter for measuring conductance and blood volume in a heart chamberof the patient. The apparatus comprises a processor for determininginstantaneous volume of the ventricle by applying a non-linearrelationship between the measured conductance and the volume of blood inthe heart chamber to identify mechanical strength of the chamber. Theprocessor is in communication with the conductance catheter.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter. There is the step of determining instantaneousvolume of the ventricle by applying a non-linear relationship betweenthe measured conductance and the volume of blood in the heart chamber toidentify mechanical strength of the chamber with a processor. Theprocessor in communication with the conductance catheter.

The present invention pertains to an apparatus for determining cardiacperformance in a patient. The apparatus comprises a conductance catheterfor measuring conductance in a heart chamber of the patient, where theconductance includes contributions from blood and muscle with respect tothe heart chamber. The apparatus comprises a processor for determininginstantaneous volume of the heart chamber by removing the musclecontribution from the conductance. The processor is in communicationwith the conductance catheter.

The present invention pertains to a method for determining cardiacperformance in a patient. The method comprises the steps of measuringconductance in a heart chamber of the patient with a conductancecatheter, where the conductance includes contributions from blood andmuscle with respect to the heart chamber. There is the step ofdetermining instantaneous volume of the heart chamber by removing themuscle contribution from the conductance with a processor, the processorin communication with the conductance catheter.

The present invention pertains to an apparatus for determining cardiacperformance in the patient. The apparatus comprises a conductancecatheter having measuring electrodes for measuring conductance in aheart chamber of the patient. The apparatus comprises a processor fordetermining instantaneous volume of the heart chamber according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, the processor in communicationwith the conductance catheter.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter having measuring electrodes. There is the step ofdetermining instantaneous volume of the ventricle according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, to identify mechanical strengthof the chamber with a processor. The processor is in communication withthe conductance catheter.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, the preferred embodiment of the inventionand preferred methods of practicing the invention are illustrated inwhich:

FIG. 1 shows a four electrode catheter in volume cuvette.

FIG. 2 is a plot for estimating parallel conductance.

FIG. 3 is a plot of apparent conductivity of cardiac muscle as afunction of frequency in CD1 mice in vivo at 37° C.

FIG. 4 shows a circuit diagram of a catheter and a measurement systemfor an open circuit load. The small triangles are the common node forthe instrument power supply.

FIG. 5 is a plot of catheter phase effects for saline solutions from 720to 10,000 μS/cm from 1 kHz to 1 MHz. Apparent conductivity (|η|) ofsaline solutions (μS/cm).

FIG. 6 is a plot of conductance vs. volume in mouse-sized calibrationcuvette.

FIG. 7 is a schematic representation of the apparatus of the presentinvention.

FIG. 8 is a cylinder-shaped murine LV model: both blood and myocardiumare modeled as cylinders.

FIG. 9 is a comparison between true volume and estimated volume by thenew and Baan's equations in FEMLAB simulations.

FIG. 10 is a comparison between true volume and estimated volume usingthe new and Baan's equations in saline experiments.

DETAILED DESCRIPTION

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIG. 7 thereof, there is shown an apparatus fordetermining cardiac performance in the patient. The apparatus comprisesa conductance catheter 12 for measuring conductance and blood volume ina heart chamber of the patient. The apparatus comprises a processor 14for determining instantaneous volume of the ventricle by applying anon-linear relationship between the measured conductance and the volumeof blood in the heart chamber to identify mechanical strength of thechamber. The processor 14 is in communication with the conductancecatheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuringinstantaneous pressure of the heart chamber in communication with theprocessor 14. The processor 14 preferably produces a plurality ofdesired wave forms at desired frequencies for the conductance catheter12. Preferably, the processor 14 produces the plurality of desired waveforms at desired frequencies simultaneously, and the processor 14separates the plurality of desired wave forms at desired frequencies theprocessor 14 receives from the conductance catheter 12. The conductancecatheter 12 preferably includes a plurality of electrodes 18 to measurea least one segmental volume of the heart chamber.

Preferably, the non-linear relationship depends on a number of theelectrodes 18, dimensions and spacing of the electrodes 18, and anelectrical conductivity of a medium in which the electrodes 18 of thecatheter 12 are disposed. The non-linear relationship may be expressedas (or a substantially similar mathematical form):

β(G)(σ=0.928 S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))

Alternatively, an approximate calibration factor may be used withsimilar accuracy of the form (or its mathematical equivalent):

β≅e^(γG) ^(h) ²

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Preferably,

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.

The pressure sensor 16 preferably is in contact with the conductancecatheter 12 to measure ventricular pressure in the chamber. Preferably,the plurality of electrodes 18 includes intermediate electrodes 20 tomeasure the instantaneous voltage signal from the heart, and outerelectrodes 22 to which a current is applied from the processor 14. Thepressure sensor 16 preferably is disposed between the intermediateelectrodes 20. Preferably, the processor 14 includes a computer 24 witha signal synthesizer 26 which produces the plurality of desired waveforms at desired frequencies and a data acquisition mechanism 28 forreceiving and separating the plurality of desired wave forms at desiredfrequencies. The computer 24 preferably converts conductance into avolume. Preferably, the computer 24 produces a drive signal having aplurality of desired wave forms at desired frequencies to drive theconductance catheter 12.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter 12. There is the step of determining instantaneousvolume of the ventricle by applying a non-linear relationship betweenthe measured conductance and the volume of blood in the heart chamber toidentify mechanical strength of the chamber with a processor 14. Theprocessor 14 in communication with the conductance catheter 12.

Preferably, there is the step of measuring instantaneous pressure of theheart chamber with a pressure sensor 16 in communication with theprocessor 14. There is preferably the step of producing a plurality ofdesired wave forms at desired frequencies for the conductance catheter12. Preferably, the producing step includes the step of producing theplurality of desired wave forms at desired frequencies simultaneously,and including the step of the processor 14 separating the plurality ofdesired wave forms at desired frequencies the processor 14 received fromthe conductance catheter 12. The producing step preferably includes thestep of producing with the processor 14 the plurality of desired waveforms at desired frequencies simultaneously.

Preferably, the determining step includes the step of applying thenon-linear relationship according to the following (or its mathematicalequivalent):

β(G)(σ=0.928 S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Or, alternatively, anapproximate geometry calibration factor may be used:

β=e^(γ[G) ^(b) ^(]) ²

where α is determined experimentally or from mathematical calculationsor numerical models.

The determining step preferably includes the step of determininginstantaneous volume according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.

Preferably, the step of measuring instantaneous pressure includes thestep of measuring instantaneous pressure with the pressure sensor 16 incontact with the conductance catheter 12 to measure the ventricularpressure in the chamber. The measuring step preferably includes the stepof measuring at least one segmental volume of the heart chamber with aplurality of electrodes 18 on the conductance catheter 12. Preferably,the measuring step includes the steps of applying a current to outerelectrodes 22 of the plurality of electrodes 18 from the processor 14,and measuring an instantaneous voltage signal from the heart withintermediate electrodes 20 of the plurality of electrodes 18.

The step of measuring instantaneous pressure preferably includes thestep of measuring instantaneous pressure with the pressure sensor 16disposed between the intermediate electrodes 20 and the outer electrodes22. Preferably, the producing with the processor 14 step includes thestep of producing with a signal synthesizer 26 of a computer 24 theplurality of desired wave forms at desired frequencies, and theprocessor 14 separating step includes the step of receiving andseparating the plurality of desired wave forms at desired frequencieswith a data acquisition mechanism 28 of the computer 24. There ispreferably the step of converting conductance into a volume with thecomputer 24. Preferably, there is the step of producing with thecomputer 24 a drive signal having the plurality of desired wave forms atdesired frequencies to drive the conductance catheter 12.

The present invention pertains to an apparatus for determining cardiacperformance in a patient. The apparatus comprises a conductance catheter12 for measuring conductance in a heart chamber of the patient, wherethe conductance includes contributions from blood and muscle withrespect to the heart chamber. The apparatus comprises a processor 14 fordetermining instantaneous volume of the heart chamber by removing themuscle contribution from the conductance. The processor 14 is incommunication with the conductance catheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuringinstantaneous pressure of the heart chamber in communication with theprocessor 14. The processor 14 preferably produces a plurality ofdesired wave forms at desired frequencies for the conductance catheter12. Preferably, the processor 14 produces the plurality of desired waveforms at desired frequencies simultaneously, and the processor 14separates the plurality of desired wave forms at desired frequencies theprocessor 14 receives from the conductance catheter 12. The processor 14preferably measures complex admittance with the conductance catheter 12to identify the muscle contribution.

Preferably, the complex admittance is defined as

Y _(p) =Gm+jωCm (Y subscript p)

where

Cm=capacitance component of muscle (F=Farads) (C subscript m)

ω=angular frequency (radians/second) (greek “omega”=2 p f)

Gm=conductance of muscle (S=Siemens) (G subscript m). The conductancepreferably is defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (S) (G subscript b).

The present invention pertains to a method for determining cardiacperformance in a patient. The method comprises the steps of measuringconductance in a heart chamber of the patient with a conductancecatheter 12, where the conductance includes contributions from blood andmuscle with respect to the heart chamber. There is the step ofdetermining instantaneous volume of the heart chamber by removing themuscle contribution from the conductance with a processor 14, theprocessor 14 in communication with the conductance catheter 12.

Preferably, there is the step of measuring instantaneous pressure of theheart chamber with a pressure sensor 16 in communication with theprocessor 14. There is preferably the step of producing a plurality ofdesired wave forms at desired frequencies for the conductance catheter12. Preferably, the producing step includes the step of producing theplurality of desired wave forms at desired frequencies simultaneously,and including the step of the processor 14 separating the plurality ofdesired wave forms at desired frequencies the processor 14 received fromthe conductance catheter 12. The producing step preferably includes thestep of producing with the processor 14 the plurality of desired waveforms at desired frequencies simultaneously. Preferably, there is thestep of measuring complex admittance with the conductance catheter 12 toidentify the muscle contribution.

The measuring the complex admittance step preferably includes the stepof measuring the complex admittance according to

Yp=Gm+jωCm (Y subscript p)

where

Cm=capacitance component of muscle (F=Farads) (C subscript m)

ω=angular frequency (radians/second) (greek “omega”=2 pi f)

Gm=conductance of muscle (S=Siemens) (G subscript m).

Preferably, the determining step includes the step of determininginstantaneous volume based on conductance defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (S) (G subscript b).

The present invention pertains to an apparatus for determining cardiacperformance in the patient. The apparatus comprises a conductancecatheter 12 for measuring conductance in a heart chamber of the patient.The apparatus comprises a processor 14 for determining instantaneousvolume of the heart chamber according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, the processor 14 incommunication with the conductance catheter 12.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter 12. There is the step of determining instantaneousvolume of the ventricle according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, to identify mechanical strengthof the chamber with a processor 14. The processor 14 is in communicationwith the conductance catheter 12.

The classic means to determine left ventricular pressure-volume (PV)relationships in patients on a beat-by-beat basis is through the use ofthe conductance (volume) catheter 12. The electric field that it createsin the human left ventricle at the time of heart catheterization is theonly technology capable of measuring instantaneous left ventricularvolume during maneuvers such as transient occlusion of the inferior venacava. Such maneuvers allow determination of the wealth of informationavailable from the PV plane including: end-systolic elastance, diastoliccompliance, and effective arterial elastance. However, use ofconductance technology in patients with dilated hearts whose LV volumescan range from 200 to 500 ml has been problematic.

The G-V method measures the conductance between electrodes 18 located inthe LV and aorta. A minimum of four electrodes 18 is required to preventthe series impedance of the electrode-electrolyte interfaces fromdistorting the measurement. Typically, the two current source-sinkelectrodes are located in the aorta and in the LV near the apex(electrodes 1 and 4 in FIG. 1). The potential difference between thepotential measuring electrodes (2 and 3) is used to calculate theconductance: G=I/V. The governing assumption is that the current densityfield is sufficiently uniform that the volume and conductance are simplyrelated by Baan's equation [1]:

$\begin{matrix}{{{Vol}(t)} = {{\left\lbrack \frac{1}{\alpha} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{G(t)} - G_{p}} \right\rbrack}} & (1)\end{matrix}$

where: α is the geometry factor (a dimensionless constant), L is thecenter-to-center distance between voltage sensing electrodes (2 and 3)(m), σ_(b) is the conductivity of blood (S/m), G(t) is the measuredinstantaneous conductance (S), and G_(p) is the parallel conductance (S)in cardiac muscle (G_(p)=0 in the calibration cuvette of FIG. 1).

Two limitations inherent in the state-of-the-art technique interferewith accurate measurements: 1) the electric field around the sensingelectrodes 18 is not uniform, leading to a non-linear relationshipbetween measured conductance and ventricular volume which has decidedlylower sensitivity to large volumes, and 2) the parallel conductancesignal added by surrounding cardiac muscle adds virtual volume to themeasurement. The new technique improves the estimate of the parallelmuscle conductance based on the measurement of complex admittance at twoor more frequencies, rather than using the admittance magnitude, as ispresently done. Furthermore, the inherent non-linearity of conductancevs. volume is usually compensated by establishing a piece-wise linearapproximation to the sensitivity curve (Vol vs. G) in the region ofoperation. That is, a is actually a function of the diameter of thevolume in FIG. 1; but is assumed constant over the operating range of ameasurement, ESV to EDV.

The electrical properties of cardiac muscle are frequency-dependent[6-14] while those of blood are not [15-18]. The admittance measurementat (at least) two frequencies can be used to separate the musclecomponent from the combined muscle-blood signal. Measurement of thephase angle of the admittance is a more sensitive indicator of themuscle signal than the magnitude of the admittance, which is currentlymeasured. Information contained in the phase angle can improve theoverall accuracy of the dual frequency admittance system. Thisreformulation of the measurement allows one to verify that the effectivesensing volume actually reaches the ventricular muscle in the case of anenlarged heart.

In the operation of the invention, the parallel conductance signal ispresently compensated by three methods: 1) hypertonic saline injection[19, 20], 2) occlusion of the inferior vena cava (IVC) [21], and 3)conductance measurement at two frequencies [22, 23]. In the firstapproach, a known volume of hypertonic saline (usually 10% NaCl) isinjected and the beat-by-beat conductance signal measured as it washesthrough the LV during several beats. The End Diastolic Conductance (EDG)is plotted against End Systolic Conductance (ESG), and the resultingline is projected back to the line of equal values (EDG=ESG when strokevolume=0), and the remainder is the estimate of parallel conductance,G_(p). (see FIG. 2.). In the second approach, occlusion of the IVC,shrinks the LV volume, but the result is analyzed in the same way asFIG. 2. The third approach attempted to use the frequency dependence ofmuscle to identify the parallel conductance [22, 23]. This is similar tothe approach described here, but different in that the particularfrequencies were limited to a maximum of about 30 kHz and only themagnitude of the combined signal was used. A maximum frequency of 100kHz is used here to better separate the muscle from the combined signal;further, the phase angle is a much more sensitive indicator of musclethan admittance magnitude alone.

Each of the parallel conductance compensation approaches has undesirablefeatures. Hypertonic saline injection creates an aphysiologicelectrolyte load that is undesirable in the failing heart. IVC occlusionbrings the ventricular free wall and septum closer to the electrodearray and artificially inflates the parallel conductance. The dualfrequency measurements are able to identify a difference signal betweenblood and cardiac muscle, but measurement using the magnitude ofadmittance alone is not sufficiently sensitive to yield satisfyingresults, and the particular frequencies used in the past are not thebest to separate the two signals. There are other considerations in thedual-frequency measurement which affect overall accuracy—notably theparasitic impedances in the catheter 12 itself—which must be compensatedbefore reliable calculations may be made. The present invention is asignificant improvement to the dual frequency method; it usesmeasurements of the complex admittance to more accurately identify theparallel muscle volume signal and does not require injecting fluids orchanging the LV volume to complete.

Frequency Dependence of Muscle Electrical Properties: Electrolyticsolutions, blood and all semiconducting materials have an electricalconductivity, σ, that is essentially independent of frequency.Dielectric materials have an electric permittivity, ∈ (F/m): in essence,permittivity is a measure of the polarizable dipole moment per unitvolume in a material [14]. A general material has both semiconductingand dielectric properties, and each aspect contributes to the totalcurrent density vector, J_(tot) (A/m²) in a vector electric field, E(V/m). The conductivity, σ, results in conduction current densityaccording to Ohm's Law, and the permittivity, ∈, contributes“displacement” current density in a harmonic (i.e. sinusoidal) electricfield, as reflected in the right hand side of Ampere's Law [40]:

J _(tot)=(σ+jω∈)E  (2)

where: j=√{square root over (−1)}, and ω=2πf=the angular frequency(r/s). J_(tot) is complex even if E is real—in other words, J and E arenot in phase with each other unless ω∈ is small with respect to σ. Mostall tissues behave as semiconductors at all frequencies below about 10MHz because σ>>ω∈. The remarkable exception is muscle tissue in vivo orvery freshly excised, [10-12, and our own unpublished measurements]. Tocalibrate this discussion, water has a very strong dipole moment, andhas a relative permittivity of around 80 at frequencies below about 1MHz; and the relative permittivities of most tissues are, therefore,usually dominated by their water content. Muscle, in contrast, has avery high relative permittivity: around 16,000 in the 10 kHz to 100 kHzrange (almost 200 times that of water) [11], owing to the trans-membranecharge distribution. Consequently, ω∈ are able to observe the frequencydependence of muscle total current density since ω∈ is larger than a forfrequencies above about 15 kHz.

For example, the apparent conductivity of murine cardiac muscle using asurface tetrapolar probe shows a reliable and repeatable frequencydependence. In FIG. 3, the indicated conductivity increasessignificantly above about 10 kHz. The conductivity in the figureincludes some permittivity effects: the measurement device actuallyindicates the magnitude of the (σ+jω∈) term in equation 2. For muscle,it is more accurate to think in terms of “admittivity”, η=σ+jω∈. σ=1,800μS/cm (0.18 S/m) from the low frequency portion of the plot, andestimate that ∈=16,000 ∈₀ (F/m) which compares well with published data.In the figure, the parasitic capacitances of the surface probe have beencompensated out using measurements of the surface probe on electrolyticsolutions with the same baseline conductivity as muscle.

Numerical Model Studies: Numerical models of the murine catheter in amouse LV were executed at volumes representative of the normal ESV andEDV in the mouse. The numerical model was an enhanced version of themodel used for the cuvette studies: each control volume (CV) could beassigned a different value of electrical conductivity, σ. The modelspatial resolution and FDM calculational approach were the same asdescribed above. A larger number of iterations were required forconvergence, however, around 400,000 iterations. This is because theelectrical boundary conditions of the inhomogeneous media substantiallyincrease the number of trials required to settle to the final solution.Models were completed using realistic volumes for ESV and EDV derivedfrom conductance catheter 12 data: 19 μl and 45 μl, respectively(ejection fraction 60%). Electrical conductivities for blood, cardiacmuscle and aorta were: σ_(b)=0.928 S/m, σ_(m)=0.0945 S/m at 10 kHz and0.128 S/m at 100 kHz, σ_(a)=0.52 S/m [41], respectively. All of theproperties are real-valued in the model—the complex nature of muscle hasnot been included in the preliminary studies. The ventricular free wallendocardial surface was treated as a smooth ellipse, and the LV wasmodeled as an ellipsoid of revolution. The geometry was considerablysimplified over the actual LV for two reasons: 1) the purpose of themodel was to identify the expected order-of-magnitude of musclecontribution to the measured conductance, 2) the resources and timeavailable did not permit development of a detailed 3-D geometry, nor theuse of more accurate finite element method (FEM) models.

Table 1 compares FDM model and experiment data. The model consistentlyunder-estimates the measured conductances: by about 11% and 35% at 10kHz, and by 30% and 47% at 100 kHz. The comparisons at 10 kHz are leastsensitive to uncertainty in tissue electrical properties and catheter 12effects. Deviations at this frequency are more likely due to geometricsimplifications in the model and under-estimation of the appropriate LVvolume to use.

TABLE 1 Summary of model and experimental conductance values (μS).Experimental data are the means of six normal mice [28], numbers inparentheses are standard deviations. Source EDV ESV FDM Model @ 10 kHz1419 μS 844 μS Experiment @ 10 kHz 1600 (500) 1300 (400) FDM Model @ 100kHz 1493 905 Experiment @ 100 kHz 2100 (400) 1700 (400)

The 100 kHz measurements reveal an additional effect due to the complexnature of the electrical properties of muscle and the effect ofcapacitance between the wires in the conductance catheter 12. While theactual values of the calculated conductance are subject to manyuncertainties, the differences between 10 kHz and 100 kHz values in themodel are due only to the electrical properties of muscle. So, in Table1 it looks at first glance as though the model work has severelyunderestimated the capacitive effects in muscle. However, it must benoted that the reported in vivo measurements do not compensate out thestray capacitance in the catheter 12 at 100 kHz. At this point, it isnot clear precisely how much of the apparent frequency-dependent signalis due to catheter 12 capacitance, and how much is due to muscle signalin those data.

The improved muscle parallel conductance compensation techniquedescribed can be implemented in existing conductance machines either inembedded analysis software (real-time or off-line processing of measureddata) or in dedicated Digital Signal Processing hardware devices.

Phase Angle Measurement: There is an embedded difficulty in thismeasurement which must be addressed: the parasitic capacitance of thecatheters has effects on the measured admittance signal phase angle inaddition to the muscle permittivity component. One necessarily measuresthe two together; and a method for compensating out or otherwise dealingwith the catheter-induced effects is required. Fortunately, all of thenecessary catheter 12 characteristics can be measured a priori. We haveidentified three approaches to this problem.

First, the catheter 12 phase angle effects stem from parasiticcapacitance between electrode wires in the catheter 12. The tetrapolarcase is relatively easy to discuss, and the multi-electrode cathetersconsist of several repeated combinations of the 4-electrode subunit. Wecan measure the six inter-electrode parasitic capacitances of the4-electrode systems (FIG. 4). The effect of the inter-electrodecapacitances can be reduced to a single capacitive admittance inparallel with the tissues, C_(cath), much larger than any of the C_(ij).This can be seen in experimental measurements on saline which has noobservable permittivity effects at frequencies below about 200 MHz;thus, all capacitance information (frequency-dependent increase in |η|,where η=σ+jω∈) in the signal comes from catheter 12 effects (FIG. 5). InFIG. 5 a small conductivity measurement probe (inter-electrodecapacitances from 60 to 70 pF) has been used to measure the apparentconductivity (|η|) of saline solutions between 720 μS/cm (lowest line)and 10,000 ηS/cm (highest line). The lines cross because the point whereσ_(NaCl)=ω∈_(cath) moves to higher frequency for higher σ. C_(cath) isapproximately 1.5 nF here.

Second, a lumped-parameter circuit model can be constructed for catheter12 effects and use this model to correct the measured potential, ΔV, tothe value it would have in the absence of the parasitic capacitances.Third, we can advance the measurement plane from the current-sourceoutput, I_(s), (FIG. 5) and voltage measurement location, ΔV, to theoutside surfaces of the four electrodes 18 using a bilinear transform.This is a standard approach in impedance measurement [see ref. 14, Ch.5] and requires only a measurement at open circuit, short circuit and anormalizing load (say, 1 kΩ) to accomplish.

The first approach is the most practical for implementation in aclinical instrument: we will subtract the catheter 12 capacitance,C_(cath), (measured a priori) from the total capacitance of themeasurement, C_(tot), with the remainder: C_(muscle)=C_(tot)−C_(cath).The measurement from 2 to 10 kHz includes only the real parts:Y₁₀=G_(b)+G_(musc). At 100 kHz:Y₁₀₀=G_(b)+G_(musc)+jω(C_(cath)+C_(musc)). Negative values are rejectedand C_(cath) is deterministic and not time-varying. The calculationstrategy is then: C_(tot)=|Y₁₀₀| sin(θ_(tot))/ω;C_(musc)=C_(tot)−C_(cath); finally,G_(p)=G_(musc)=σ_(m)C_(musc)/∈_(musc) (from the well knownconductance-capacitance analogy [40]) and G_(p) can be subtracted from|Y₁₀| to determine G_(b)—i.e. |Y₁₀|=G_(b)+G_(p). A purely analogapproach to this measurement is impossible, and a mixed signal approachwith extensive digital processing required for both catheter 12compensation and phase measurement is used. Based on the model trendsand measured values of Table 1, it is estimated the relative phaseangles in the measured admittance ought to be approximately 4° for EDVand 8° for ESV. The larger phase angle for ESV reflects the change inrelative proximity of the LV wall.

The non uniformity of the electrode sensing field is inherent in thesingle current source electrode geometry of FIG. 1. Two limiting casesillustrate the origin of this. First, for a sufficiently large cuvetteor blood volume, the electric and current density fields surroundingelectrodes 1 and 4 are similar in overall shape to those of a currentdipole: the magnitude of the current density decreases with the cube ofthe radius. At very large volume the voltage measured between electrodes2 and 3 is insensitive to the location of the outer boundary.Consequently, the measured conductance saturates at large volumes sincethe sensitivity, ΔG/ΔVol=0, and thus α=zero. Second, the other limit isreached when the outer radius of the volume is minimally larger than thecatheter 12 itself. In that case the current density approaches auniform distribution and α approaches 1. Radii between these limitscross over from α=1 to α=0.

The behavior of α was studied in experiments and numerical models of amouse-sized 4-electrode conductance catheter 12 in a volume-calibrationcuvette. This catheter 12 has L=4.5 mm between the centers of electrodes2 and 3 and is 1.4 F (i.e. 0.45 mm in diameter). The cuvette was filledwith 1 M saline solution (σ=1.52 S/m at room temperature). The resultsare summarized in FIG. 3. In the Figure, “Ideal G” is the line α=1. Thenumerically calculated (squares) and measured (circles) conductance inμS are plotted vs. cuvette volume (μl). The measurement sensitivity,ΔG/ΔVol, in the figure=α(σ/L²), and this slope asymptotically approaches0 for volumes greater than about 150 μl for this catheter 12. Thisbehavior is determined solely by the geometry of the current densityfield, and α is independent of the conductivity of the solution.

Based on the numerical model and experimental results, a new calibrationequation using β(G) as the geometry calibration function to replace a inequation 4:

$\begin{matrix}{{{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}} & (4)\end{matrix}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel “leakage”admittance, dominated by cardiac muscle. At small volumes, β(G)=α=1. Atlarge volumes, β(G) increases without bound, as expected from the modelwork in FIG. 6. The new calibration function includes the non-linearnature of the volume calculation: since for a particular catheter β(G)depends on the conductivity of the liquid and on measured G—i.e. oncuvette and/or ventricular blood outer radius—it is not simplyexpressible in terms of 1/α. The expression for β(G) for the mouse-sizedcatheter 12 described above for FIG. 6 data is:

β(G)(σ=0.928 S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))  (5)

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Here β(G) depends only on thereal part of Y because the cuvette measurements do not contain muscle.In use, G is the real part of [Y(t)−Y_(p)], and any imaginary part ofthe signal is rejected since it must come from a muscle component, orfrom the instrumentation. As required, β(G) approaches 1 as G becomessmall compared to the asymptote, 2057 μS.

The improved calibration method can be implemented in existingconductance machines either in embedded analysis software (real-time oroff-line processing of measured data) or in dedicated Digital SignalProcessing hardware devices.

Complex admittance in regard to overall admittance as it relates toY(t)−Y_(p) is as follows.

Y(t)=Gb+Gm+jωCm

Y _(p) =Gm+jωCm(Y _(p))

C_(m)=capacitance component of muscle (F=Farads) (C_(m))

ω=angular frequency (radians/second) (s=2 π f)

Gm=conductance of muscle (S=Siemens) (G_(m))

Gb=conductance of blood (S) (G_(b))

Y(t)=total instantaneous measured admittance (S) (after catheter 12effects have been compensated.Y_(p)=total parallel admittance (everything but blood). The cardiacmuscle dominates Y_(p); and thus once Y_(p) is known (from themeasurement of phase angle—only muscle has capacitance and contributesto the phase angle) the estimate of G_(b) can be improved and thus thevolume of blood.

The following elaborates on the nonlinear relationship β(G) betweenconductance and volume.

1. Physical Principle:

β(G) is a nonlinear function for every admittance (conductance) catheter12. The function depends on the number, dimensions and spacing of theelectrodes 18 used, and on the electrical conductivity of the mediumwhich it is in. β(G) is determined by the shape of the current fieldcreated by the electrodes 18.

2. Experimental Determination

β(G) may be determined experimentally for any conductance catheter 12 incylindrical “cuvettes” in which a solution of known electricalconductivity is measured over a range of cuvette diameters. The “volume”is the volume of solution between the voltage sensing electrodes 18.

3. Determination by Solution of the Electric Field Equations

β(G) may also be determined by solving the governing electric fieldequations, namely Gauss' Electric Law—either in integral form or in theform of the Laplace at low frequency, and the wave equations at highfrequency—subject to appropriate boundary conditions. The solution maybe by analytical means (paper and pencil) or by numerical means, as in adigital computer 24 model of the electric and/or electromagnetic fields.For any current field established by two or more electrodes 18 a modelyields the measured conductance when the total current—surface integralof (sigma mag(E) dot product dS), where dS is the elemental area—isdivided by the measurement electrode voltage, from the model orcalculation results. Many books on electromagnetic field theory teachhow to make the calculation. A specific reference is Chapter 6 (p. 184)in W. H. Hayt and J. A. Buck “Engineering Electromagnetics”, 6th EditionMcGraw-Hill, Boston, 2001, incorporated by reference herein. Thespecific reference teaches how to calculate resistance, R, butconductance, G is simply the reciprocal of R, G=1/R. The calculated Gmay be a complex number (for mixed materials like tissues), in whichcase the catheter 12 measures “admittance”, Y, a complex number.

(A) Measured Conductance and Capacitance Signals

Two of the catheter electrodes (#1 and #4) are used to establish acurrent field in the ventricle. The current field results in an electricfield in the tissues, the strength of which is determined by measuringthe voltage between electrodes #2 and #3. Because electrodes 2 and 3carry negligible amounts of current, they provide a useful estimate ofthe electric field in the tissues. The current supplied to the tissue(electrodes 1 and 4) is divided by the voltage measured betweenelectrodes 2 and 3 to determine the admittance of the tissue, Y (S). Theadmittance consists of two parts, the Conductance, G (S) the real part,and the Susceptance, B (S), the imaginary part: Y=G+jB. In thismeasurement, both blood and muscle contribute to the real part of themeasured signal, G=G_(b)+G_(musc). However, after all catheter-inducedeffects have been removed, only the muscle can contribute to theimaginary part, B=jωC_(musc).

For any geometry of electric field distribution in a semiconductingmedium, the conductance may be calculated from:

$\begin{matrix}{G = {\frac{I}{V} = \frac{\underset{S}{\int\int}\ \sigma \; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot \ {l}}}}}} & (a)\end{matrix}$

where the surface, S, in the numerator is chosen to enclose all of thecurrent from one of the electrodes used to establish the electric field,E, and the integration pathway in the denominator is from the lowvoltage “sink” electrode at position “a” to the higher voltage “source”electrode at position “b”. Similarly, for any geometry of electric fieldin a dielectric medium, the capacitance may be calculated from:

$\begin{matrix}{C = {\frac{Q}{V} = \frac{\underset{S}{\int\int}\ ɛ\; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot \ {l}}}}}} & (b)\end{matrix}$

B) Parallel Admittance in the Cardiac Muscle

The measured tissue signal, Y=G_(b)+G_(musc)+jωC_(musc). From the highfrequency measurement C_(musc) may be determined from the measured phaseangle by: C_(musc)=|Y| sin(θ)/ω after catheter phase effects have beenremoved. By equations (a) and (b) above, the muscle conductance can bedetermined from its capacitance by: G_(musc)=σ/∈C_(musc) since the twoequations differ only by their respective electrical properties—i.e. theelectric field geometry calculations are identical in a homogeneousmedium. In this way, the muscle conductance (independent of frequency,and thus the same in the low frequency and high frequency measurements)may be determined from the muscle capacitance (observable only in thehigh frequency measurements).

Beyond these very general relations, a person may make catheterelectrode configurations of many shapes and sizes and use them in manysorts of conductive solutions. All would have a different β(G) function.

In an alternative embodiment, the LV volume signal is only relative toLV blood conductance, but the measured admittance comes from both bloodand myocardium. Therefore, it is desired to extract the bloodconductance from the measured admittance, which can be done by using theunique capacitive property of myocardium. To achieve it, the first stepis to obtain the conductivity and permittivity of myocardium.

Myocardial Conductivity and Permittivity

It is believed that blood is only conductive, while myocardium is bothconductive and capacitive. Therefore, the measured frequency-dependentmyocardial “admittivity”, Y′_(m)(f), actually is composed of twocomponents:

Y′ _(m)(f)=√{square root over (σ_(m) ²+(2πf∈ _(r)∈₀)²)}  (6)

where σ_(m) is the real myocardial conductivity, f is frequency, ∈_(r)is the relative myocardial permittivity, and ∈₀ is the permittivity offree space. Experimentally, Y′_(m)(f) can be measured at two differentfrequencies, such as 10 and 100 kHz, and then the value of σ_(m) andmyocardial permittivity ∈ can be calculated by:

$\begin{matrix}{\sigma_{m} = \sqrt{\frac{{100 \cdot \left\lbrack {Y_{m}^{\prime}\left( {10\mspace{14mu} k} \right)} \right\rbrack^{2}} - \left\lbrack {Y_{m}^{\prime}\left( {100\mspace{14mu} k} \right)} \right\rbrack^{2}}{99}}} & (7) \\{{ɛ \equiv {ɛ_{r}ɛ_{0}}} = {\frac{1}{2\; {\pi \cdot 10^{4}}}\sqrt{\frac{\left. {Y_{m}^{\prime}\left( {10\mspace{14mu} k} \right)} \right\rbrack^{2} - \left\lbrack {Y_{m}^{\prime}\left( {10\mspace{14mu} k} \right)} \right\rbrack^{2}}{99}}}} & (8)\end{matrix}$

Blood Conductance

In the 10 and 100 kHz dual-frequency measurement system, the measuredmagnitude of admittance, |Y(f)|, is blood conductance (g_(b)) inparallel with myocardial conductance (g_(m)) and capacitance (C_(m)),shown as

|Y(10k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}{squareroot over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}  (9)

|Y(100k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁵ C_(m))²)}{square root over ((g _(b) +g _(m))²+(2π·10⁵ C _(m))²)}  (10)

Using equations (9) and (10),

$\begin{matrix}{C_{m} = {\frac{1}{2\; {\pi \cdot 10^{4}}}\sqrt{\frac{{{Y\left( {100\mspace{14mu} k} \right)}}^{2} - {{Y\left( {10\mspace{14mu} k} \right)}}^{2}}{99}}}} & (11) \\{{g_{b} + g_{m}} = \sqrt{\frac{{100 \cdot {{Y\left( {10\mspace{14mu} k} \right)}}^{2}} - {{Y\left( {100\mspace{14mu} k} \right)}}^{2}}{99}}} & (12)\end{matrix}$

From the well known conductance-capacitance analogy [40],

$\begin{matrix}{g_{m} = {C_{m}\frac{\sigma_{m}}{ɛ}}} & (13)\end{matrix}$

Substitute eq. (13) into eq. (12), blood conductance g_(b) is obtainedas

$\begin{matrix}{g_{b} = {\left( {\cdot \sqrt{\frac{{100 \cdot {{Y\left( {10\mspace{14mu} k} \right)}}^{2}} - {{Y\left( {100\mspace{14mu} k} \right)}}^{2}}{99}}} \right) - g_{m}}} & (14)\end{matrix}$

A new conductance-to-volume conversion equation is

Vol(t)=ρ_(b) L ² g _(b)(t)exp[γ·(g _(b)(t))²]  (15)

where Vol(t) is the instantaneous volume, ρ_(b) is the bloodresistivity, L is the distance between the sensing electrodes, g_(b)(t)is the instantaneous blood conductance, and γ is an empiricalcalibration factor, which is determined by the following steps.

-   -   1. A flow probe is used to measure the LV stroke volume (SV),        denoted as SV_(flow).    -   2. Assign an initial positive number to γ, and use equation (15)        to convert blood conductance to volume signal. The resulting        stroke volume is denoted as SVγ.    -   3. If SVγ is smaller than SV_(flow), increase the value of γ.        Otherwise, decrease it.    -   4. Repeat steps 2 and 3 until it satisfies.

SVγ−SV_(flow)  (16)

-   -    Since equation (15) is a monotonic increasing function, there        is only one possible positive solution for γ.

This empirical factor γ is used to compensate and calibrate the overalluncertainty and imperfection of the measurement environment, such asinhomogeneous electrical field and off-center catheter position.

Simulation Results

A commercial finite element software, FEMLAB, is used to simulate thisproblem. A simplified LV model is created by modeling both LV blood andmyocardium as cylinders with a four-electrode catheter inserted into thecenter of cylinders, as shown in FIG. 8.

The radius of the inner blood cylinder was changed to explore therelationship between volume and conductance. Assuming stroke volume isthe difference between the largest and smallest blood volume, and thisdifference is used to determine the empirical calibration factors, α andγ, for Baan's and the new equations respectively. The calculatedmagnitude of admittance, blood conductance, true volume, and estimatedvolume by Baan's and the new equations are listed in Table II and alsoplotted in FIG. 9, where the true volume is the volume between the twoinner sensing electrodes. The distance between two inner sensingelectrodes for a mouse size catheter is 4.5 mm.

TABLE II Comparison of true and estimated volume by two equationsEstimated Calculated volume by Estimated magnitude of Blood Baan'svolume by admittance conductance True volume equation new equation (μS)(μS) (μL) (μL) (μL) 2491.1 2344.7 62.9 64.5 62.0 2030.2 1853.3 43.7 51.043.1 1514.0 1314.3 28.0 36.2 27.5 1337.7 1133.5 23.5 31.2 23.0 1162.4956.1 19.4 26.3 19.0 992.5 786.4 15.7 21.6 15.3 829.3 626.2 12.4 17.212.0 677.3 479.3 9.5 13.2 9.1 538.1 347.9 7.0 9.6 6.6 414.4 234.2 4.96.4 4.4

In Vitro Saline Experiments

Several cylinder holes were drilled in a 1.5-inch thick block ofPlexiglas. The conductivity of saline used to fill those holes was 1.03S/m made by dissolving 0.1 M NaCl in 1 liter of water at 23° C. roomtemperature, which is about the blood conductivity. A conductancecatheter with 9 mm distance between electrodes 2 and 3 is used tomeasure the conductance.

Since plexiglas is an insulating material, the measured conductancecomes from saline only, not from the plexiglas wall. Therefore, themeasured saline conductance corresponds to the blood conductance in vivoexperiments. Again, stroke volume is assumed to be the differencebetween the largest and smallest blood volume, and then used todetermine the empirical calibration factors, α and γ, for Baan's and thenew equations, respectively. The measured data at 10 kHz and theestimated volume by Baan's and the new equations are listed in TableIII. The true volume listed is the volume between electrodes 2 and 3.The data are plotted in FIG. 10.

TABLE III Comparison of true and estimated volume in the drilled holesEstimated volume by Estimated Diameter of Measured Baan's volume byDrilled holes conductance True volume equation new equation (inch) (μS)(μL) (μL) (μL) 3/16 1723.5 160.3 562.0 160.5 ¼ 2675.0 285.0 872.3 310.35/16 3376.0 445.3 1100.9 494.5 ⅜ 3836.4 641.3 1251.0 684.8 7/16 4171.0827.9 1360.1 866.7 ½ 4394.3 1140.1 1432.9 1031.2

It is found that the resulting volumes obtained from the new equationare much closer to the MRI data, which is believed to be the truth.However, more noise is found in a larger volume by the new method,observed in FIG. 11. The reason is that as the volume increases, theexponential term of the new equation would amplify the noise morerapidly than the linear Baan's equation.

Although the invention has been described in detail in the foregoingembodiments for the purpose of illustration, it is to be understood thatsuch detail is solely for that purpose and that variations can be madetherein by those skilled in the art without departing from the spiritand scope of the invention except as it may be described by thefollowing claims.

APPENDIX

The following is a list of references, identified herein, all of whichare incorporated by reference herein.

1. An apparatus for determining cardiac performance in the patientcomprising: a conductance catheter for measuring conductance and bloodvolume in a heart chamber of the patient; and a processor fordetermining instantaneous volume of the ventricle by applying anon-linear relationship between the measured conductance and the volumeof blood in the heart chamber to identify mechanical strength of thechamber, the processor in communication with the conductance catheter.2. An apparatus as described in claim 1 including a pressure sensor formeasuring instantaneous pressure of the heart chamber in communicationwith the processor.
 3. An apparatus as described in claim 2 wherein theprocessor produces a plurality of desired wave forms at desiredfrequencies for the conductance catheter.
 4. An apparatus as describedin claim 3 wherein the processor produces the plurality of desired waveforms at desired frequencies simultaneously, and the processor separatesthe plurality of desired wave forms at desired frequencies the processorreceives from the conductance catheter.
 5. An apparatus as described inclaim 4 wherein the conductance catheter includes a plurality ofelectrodes to measure a least one segmental volume of the heart chamber.6. An apparatus as described in claim 5 wherein the non-linearrelationship depends on a number of the electrodes, dimensions andspacing of the electrodes, and an electrical conductivity of a medium inwhich the electrodes of the catheter are disposed.
 7. An apparatus asdescribed in claim 6 wherein the non-linear relationship isβ(G)(σ=0.928 S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is themeasured conductance (S), the calculations have been corrected to theconductivity of whole blood at body temperature (0.928 S/m), and 2057 isthe asymptotic conductance in μS when the cuvette is filled with a largevolume of whole blood.
 8. An apparatus as described in claim 7 wherein${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.
 9. An apparatus as described inclaim 8 wherein the pressure sensor is in contact with the conductancecatheter to measure ventricular pressure in the chamber.
 10. Anapparatus as described in claim 9 wherein the plurality of electrodesincludes intermediate electrodes to measure and instantaneous voltagesignal from the heart, and outer electrodes to which a current isapplied from the processor.
 11. An apparatus as described in claim 10wherein the pressure sensor is disposed between the intermediateelectrodes and the outer electrodes.
 12. An apparatus as described inclaim 11 wherein the processor includes a computer with a signalsynthesizer which produces the plurality of desired wave forms atdesired frequencies and a data acquisition mechanism for receiving andseparating the plurality of desired wave forms at desired frequencies.13. An apparatus as described in claim 12 wherein the computer convertsconductance into a volume.
 14. An apparatus as described in claim 13wherein the computer produces a drive signal having a plurality ofdesired wave forms at desired frequencies to drive the conductancecatheter.
 15. An apparatus as described in claim 6 whereinVol(t)=ρL ² g _(b)(t)exp[γ·(g _(b)(t))²] where Vol(t) is theinstantaneous volume, ρ is the blood resistivity, L is the distancebetween the sensing electrodes, g_(b)(t) is the instantaneous bloodconductance, and γ is an empirical calibration factor.
 16. A method fordetermining cardiac performance in the patient comprising the steps of:measuring conductance and blood volume in a heart chamber of the patientwith a conductance catheter; and determining instantaneous volume of theventricle by applying a non-linear relationship between the measuredconductance and the volume of blood in the heart chamber to identifymechanical strength of the chamber with a processor, the processor incommunication with the conductance catheter.
 17. A method as describedin claim 16 including the step of measuring instantaneous pressure ofthe heart chamber with a pressure sensor in communication with theprocessor.
 18. A method as described in claim 17 including the step ofproducing a plurality of desired wave forms at desired frequencies forthe conductance catheter.
 19. A method as described in claim 18 whereinthe producing step includes the step of producing the plurality ofdesired wave forms at desired frequencies simultaneously, and includingthe step of the processor separating the plurality of desired way formsat desired frequencies the processor received from the conductancecatheter.
 20. A method as described in claim 19 wherein the producingstep includes the step of producing with the processor the plurality ofdesired wave forms at desired frequencies simultaneously.
 21. A methodas described in claim 20 wherein the determining step includes the stepof applying the non-linear relationship according toβ(G)(σ=0.928 S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is themeasured conductance (S), the calculations have been corrected to theconductivity of whole blood at body temperature (0.928 S/m), and 2057 isthe asymptotic conductance in μS when the cuvette is filled with a largevolume of whole blood.
 22. A method as described in claim 21 wherein thedetermining step includes the step of determining instantaneous volumeaccording to${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.
 23. A method as described inclaim 22 wherein the step of measuring instantaneous pressure includesthe step of measuring instantaneous pressure with the pressure sensor incontact with the conductance catheter to measure the ventricularpressure in the chamber.
 24. A method as described in claim 23 whereinthe measuring step includes the step of measuring at least one segmentalvolume of the heart chamber with a plurality of electrodes on theconductance catheter.
 25. A method as described in claim 24 wherein themeasuring step includes the steps of applying a current to outerelectrodes of the plurality of electrodes from the processor, andmeasuring an instantaneous voltage signal from the heart withintermediate electrodes of the plurality of electrodes.
 26. A method asdescribed in claim 25 wherein the step of measuring instantaneouspressure includes the step of measuring instantaneous pressure with thepressure sensor disposed between the intermediate electrodes and theouter electrodes.
 27. An apparatus as described in claim 26 wherein theproducing with the processor step includes the step of producing with asignal synthesizer of a computer the plurality of desired wave forms atdesired frequencies, and the processor separating step includes the stepof receiving and separating the plurality of desired wave forms atdesired frequencies with a data acquisition mechanism of the computer.28. A method as described in claim 27 including the step of convertingconductance into a volume with the computer.
 29. A method as describedin claim 28 including the step of producing with the computer a drivesignal having the plurality of desired wave forms at desired frequenciesto drive the conductance catheter.
 30. A method as described in claim 19wherein the determining step includes the step of determininginstantaneous volume according toVol(t)=ρL ² g _(b)(t)exp[γ·(g _(b)(t))²] where Vol (t) is theinstantaneous volume, σ_(b) is the blood resistivity, L is the distancebetween the sensing electrodes, g_(b)(t) is the instantaneous bloodconductance, and γ is an empirical calibration factor.
 31. An apparatusfor determining cardiac performance in a patient comprising: aconductance catheter for measuring conductance in a heart chamber of thepatient, where the conductance includes contributions from blood andmuscle with respect to the heart chamber; and a processor fordetermining instantaneous volume of the heart chamber by removing themuscle contribution from the conductance, the processor in communicationwith the conductance catheter.
 32. An apparatus as described in claim 31including a pressure sensor for measuring instantaneous pressure of theheart chamber in communication with the processor.
 33. An apparatus asdescribed in claim 32 wherein the processor produces a plurality ofdesired wave forms at desired frequencies for the conductance catheter.34. An apparatus as described in claim 33 wherein the processor producesthe plurality of desired wave forms at desired frequenciessimultaneously, and the processor separates the plurality of desiredwave forms at desired frequencies the processor receives from theconductance catheter.
 35. An apparatus as described in claim 34 whereinthe processor measures complex admittance with the conductance catheterto identify the muscle contribution.
 36. An apparatus as described inclaim 35 wherein the complex admittance is defined asYp=Gm+jωCm (Y subscript p) where Cm=capacitance component of muscle(F=Farads) (C subscript m) ω=angular frequency (radians/second) (greek“omega”=2 pi f) Gm=conductance of muscle (S=Siemens) (G subscript m).37. An apparatus as described in claim 36 wherein the conductance isdefined asY(t)=Gb+Gm+jωCm where Gb=conductance of blood (S) (G subscript b).
 38. Amethod for determining cardiac performance in a patient comprising:measuring conductance in a heart chamber of the patient with aconductance catheter, where the conductance includes contributions fromblood and muscle with respect to the heart chamber; and determininginstantaneous volume of the heart chamber by removing the musclecontribution from the conductance with a processor, the processor incommunication with the conductance catheter.
 39. A method as describedin claim 38 including the step of measuring instantaneous pressure ofthe heart chamber with a pressure sensor in communication with theprocessor.
 40. A method as described in claim 39 including the step ofproducing a plurality of desired wave forms at desired frequencies forthe conductance catheter.
 41. A method as described in claim 40 whereinthe producing step includes the step of producing the plurality ofdesired wave forms at desired frequencies simultaneously, and includingthe step of the processor separating the plurality of desired wave formsat desired frequencies the processor received from the conductancecatheter.
 42. A method as described in claim 41 wherein the producingstep includes the step of producing with the processor the plurality ofdesired wave forms at desired frequencies simultaneously.
 43. A methodas described in claim 42 including the step of measuring complexadmittance with the conductance catheter to identify the musclecontribution.
 44. A method as described in claim 43 wherein themeasuring the complex admittance step includes the step of measuring thecomplex admittance according toYp=Gm+jωCm (Y subscript p) where Cm=capacitance component of muscle (FFarads) (C subscript m) ω=angular frequency (radians/second) (greek“omega”=2 pi f) Gm=conductance of muscle (S=Siemens) (G subscript m).45. A method as described in claim 44 wherein the determining stepincludes the step of determining instantaneous volume based onconductance defined asY(t)=Gb+Gm+jωCm where Gb=conductance of blood (S) (G subscript b). 46.An apparatus for determining cardiac performance in the patientcomprising: a conductance catheter for measuring conductance in a heartchamber of the patient; and a processor for determining instantaneousvolume of the heart chamber according to${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, the processor in communicationwith the conductance catheter.
 47. A method for determining cardiacperformance in the patient comprising the steps of: measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter; and determining instantaneous volume of theventricle according to${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack\left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, to identify mechanical strengthof the chamber with a processor, the processor in communication with theconductance catheter.